To determine which proportion correctly represents the cost of the crackers, let's examine each of the provided proportions step-by-step and verify which one holds true.
1. Proportion: [tex]\(\frac{1}{1.75} = \frac{3}{5.25}\)[/tex]
- Calculate the left-hand side:
[tex]\[
\frac{1}{1.75} = \frac{1}{1.75} \approx 0.5714
\][/tex]
- Calculate the right-hand side:
[tex]\[
\frac{3}{5.25} = \frac{3}{5.25} \approx 0.5714
\][/tex]
- Both sides are equal ([tex]\(0.5714 \approx 0.5714\)[/tex]), so this proportion is true.
2. Proportion: [tex]\(\frac{1}{1.75} = \frac{5.25}{3}\)[/tex]
- Calculate the right-hand side:
[tex]\[
\frac{5.25}{3} = \frac{5.25}{3} \approx 1.75
\][/tex]
- Compare to the left-hand side:
[tex]\[
\frac{1}{1.75} \approx 0.5714 \quad \text{(as before)}
\][/tex]
- The sides are not equal ([tex]\(0.5714 \neq 1.75\)[/tex]), so this proportion is false.
3. Proportion: [tex]\(\frac{1.75}{1} = \frac{3}{5.25}\)[/tex]
- Calculate the left-hand side:
[tex]\[
\frac{1.75}{1} = 1.75
\][/tex]
- Compare to the right-hand side:
[tex]\[
\frac{3}{5.25} \approx 0.5714 \quad \text{(as before)}
\][/tex]
- The sides are not equal ([tex]\(1.75 \neq 0.5714\)[/tex]), so this proportion is false.
4. Proportion: [tex]\(\frac{5.25}{1.75} = \frac{1}{3}\)[/tex]
- Calculate the left-hand side:
[tex]\[
\frac{5.25}{1.75} \approx 3
\][/tex]
- Compare to the right-hand side:
[tex]\[
\frac{1}{3} \approx 0.3333
\][/tex]
- The sides are not equal ([tex]\(3 \neq 0.3333\)[/tex]), so this proportion is false.
After examining all the given proportions, we find that the only true proportion is:
[tex]\[
\boxed{\frac{1}{1.75} = \frac{3}{5.25}}
\][/tex]
